This article contains data concerning the movement of extra-EU asylum seekers in Europe. Data used in this paper were collected from the Eurostat database and the UNHCR database. The data consist of some socio-economic features related to 30 European countries where extra-EU asylum seekers have applied for protection. All variables were transformed into their natural logs. The degree of statist...

Abstract Let $G_1, \ldots , G_k$ be finite-dimensional vector spaces over a prime field $\mathbb {F}_p$ . A multilinear variety of codimension at most $d$ is subset $G_1 \times \cdots defined as the zero set forms, each which on some coordinates. map $\phi$ $B$ if for coordinate $c$ and all choices $x_i \in G_i$ $i\not =c$ restriction $y \mapsto \phi (x_1, x_{c-1}, y, x_{c+1}, x_k)$ linear wher...

We develop and study the complexity of propositional proof systems of varying strength extending resolution by allowing it to operate with disjunctions of linear equations instead of clauses. We demonstrate polynomial-size refutations for hard tautologies like the pigeonhole principle, Tseitin graph tautologies and the clique-coloring tautologies in these proof systems. Using the (monotone) int...

The analysis of multilinear singular integrals has much of its origins in several works by Coifman and Meyer in the 70’s; see for example [3]. More recently, in [4] and [5], an updated systematic treatment of multilinear singular integral operators of Calderón-Zygmund type was presented in light of some new developments. See also [6] and the references therein for a detailed description of prev...

Kabanets and Impagliazzo [KI04] show how to decide the circuit polynomial identity testing problem (CPIT) in deterministic subexponential time, assuming hardness of some explicit multilinear polynomial family {fm}m≥1 for arithmetic circuits. In this paper, a special case of CPIT is considered, namely non-singular matrix completion (NSMC) under a low-individual-degree promise. For this subclass ...

Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor completion. The most challenging problem is related to determination of model complexity (i.e., multilinear rank), especially when noise and missing data are present. In addition, existing meth...

Tenenbuam and Freeman proposed bilinear classifiers as a tool to classify observations influenced by both the variable to classify (“content”) and a nuisance factor (“style”). In most real-world problem however, observations are influenced by a number of such factors. Gait identification is a typical such situation. To tackle their influence, it is natural to resort to multilinear or tensor dec...

As the development of singular integral operators, their commutators and multilinear operators have been well studied (see [4, 5, 6, 7, 8, 9, 10]). In [4, 5, 6, 7, 8, 9, 10], the authors prove that the commutators and multilinear operators generated by the singular integral operators and BMO functions are bounded on L(R) for 1 < p <∞; Chanillo (see [2]) proves a similar result when singular int...

We consider global optimization of nonconvex problems containing multilinear functions. It is well known that the convex hull of a multilinear function over a box is polyhedral, and the facets of this polyhedron can be obtained by solving a linear optimization problem (LP). When used as cutting planes, these facets can significantly enhance the quality of conventional relaxations in general-pur...

We provide constructions of multilinear groups equipped with natural hard problems from indistinguishability obfuscation, homomorphic encryption, and NIZKs. This complements known results on the constructions of indistinguishability obfuscators from multilinear maps in the reverse direction. We provide two distinct, but closely related constructions and show that multilinear analogues of the DD...